Complex Numbers (Book)

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Complex Numbers

Complex Numbers

A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.

The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.

Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.

Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.

http://www.ddewey.net/mandelbrot/

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Brandiwyn🎶

a day ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

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JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

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Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

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Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

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Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

October 1, 2020 at 12:06am

#994739

Wasted

Let's open October with a prompt from

Journalistic Intentions

(18+)
This is for the journal keeping types that come to PLAY! New round starts July 1!
#2213121 by Turkey DrumStik

This round will focus on weird names! I have worked in fields that have given me access to many bizarre names over the years. They are short prompts for a reason. I really want to see participants flex their mental muscles this round!

I'm not sure if my mental muscles are up to the task. They'd rather sit at home and drink. But I'm going to pick one of these prompts at random and see where it leads me.

Solid Waste Rd.

(You can see the other eccentric road names, as well as the other prompts, at the contest link above.)

I like roads.

Hell, I've designed roads.

Not major ones or anything, but those curvy little subdivision roads with their cul-de-sacs and cookie-cutter houses. I wasn't responsible for the houses. I was only responsible for making sure they weren't going to flood after they were built. Anytime you add impervious surface to an area -- roads, sidewalks, driveways, patios, the houses themselves -- stormwater runoff increases. I'll spare you the details, but the reason why shouldn't be too obscure.

But even runoff coming in from offsite can be an issue, so you don't plan to put houses where this is going to happen. Otherwise, next big storm comes along and your house gets washed downstream. It becomes, in effect, solid waste.

But that's not what I suspect Solid Waste Road was named after.

The other reason I like roads is I like driving on them. They go places and present you with things to look at -- sometimes big things like mountains or deserts, and sometimes little things like street signs.

Because sometimes, as this prompt illustrates, the street signs themselves can be oddball, eccentric, amusing, or head-scratching.

I always wonder what streets and roads are named for. Sometimes, it's trivial, like 33rd Street in Manhattan. Sometimes it's obvious, like Main Street in... well, just about any town in the US. But sometimes, it's a mystery to be solved.

There's a road near me called Turkey Sag Road, for instance. This bugged me until someone pointed out to me that the "sag" part was etymologically related to the "sac" in "cul-de-sac," which means, in French... wait for it... you're not going to believe this in a million years... "sack." Not sure how factual that information was, though.

And yet, I still don't know whether it's named for a hollow where turkeys hung out, or whether someone along the road used to sack turkeys for Thanksgiving or whatever. The internet is completely useless in this regard, and the few people who live in old houses on enormous plots of land along said road do not seem to be the kind who welcome strangers knocking on their doors to ask stupid questions.

Two of my favorite road names are, in no particular order, Clint Drive and Flicker Lane.

I'm sure this makes no sense on the face of it. Perfectly ordinary words or names, right?

Except consider that road names are almost exclusively etched onto street signs in BLOCK CAPS.

And do you know what you get when you put an L and an I together in BLOCK CAPS?

There's an old warning for comics writers, because comics dialogue was also traditionally done in block caps: Never, ever, ever name a character CLINT FLICKER.

Anyway, I'm going to save some of my other road name musings on the chance I'll pick one of the other weird road names in a future entry. I'll just leave you with this: I'd bet $10 that Solid Waste Road leads to the local sewage treatment facility, because that's what they call anything that goes through the sewer system that isn't, well, liquid. And sometimes the stuff that is liquid, but then settles out. It's very tempting to call that "shit," and I suppose in the very general sense of the term it is (as in "What's all this shit?") but actual fecal matter isn't all that's there. No, there's toilet paper, obviously; some of your kids' toys; "flushable" wipes that really aren't; and your ex's wedding ring.

Or it could be a dump, or "landfill." Either way, it's solid waste.

So it's not all that bizarre, really; perhaps someone considered it a bit of a joke ("Okay, we can't call it "Shit Lane," and "Treatment Plant Drive" won't fit on the street sign, so..."); but I'll admit it would be amusing to drive past and see the sign. Still, while it's likely in an industrial-zoned area, I feel a good bit of sympathy for any humans who live along that road. Not only do they have to put up with the fragrance of a dump or a treatment plant, but anyone who sends them snail mail can get a great chuckle at their expense.

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